论文标题
拐角处的角域上有非恒定涡度的角域上的2D Euler方程的唯一性
Uniqueness of the 2D Euler equation on a corner domain with non-constant vorticity around the corner
论文作者
论文摘要
我们考虑到角域上的2D不可压缩的Euler方程，带有$ \ frac {1} {2} {2} <ν<ν<1 $的角度$νπ$。我们证明，如果初始涡度$ω_0\ in l^{1}（ω）\ cap l^{\ infty}（ω）$，并且如果$ω_0$是非负的，并且在域的角度双歧器的一侧支持，则弱解决方案是独一无二的。这是当速度远离Lipschitz远的情况下证明独特性并且初始涡度在边界周围并非繁琐时，这是第一个结果。
We consider the 2D incompressible Euler equation on a corner domain $Ω$ with angle $νπ$ with $\frac{1}{2}<ν<1$. We prove that if the initial vorticity $ω_0 \in L^{1}(Ω)\cap L^{\infty}(Ω)$ and if $ω_0$ is non-negative and supported on one side of the angle bisector of the domain, then the weak solutions are unique. This is the first result which proves uniqueness when the velocity is far from Lipschitz and the initial vorticity is nontrivial around the boundary.
